SOLUTION: find the length of the hypotenuse of the right triangle, side a=25, side b=12

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Question 316018: find the length of the hypotenuse of the right triangle, side a=25, side b=12
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

We basically have this triangle set up:





To find the unknown length, we need to use the Pythagorean Theorem.


Remember, the Pythagorean Theorem is a%5E2%2Bb%5E2=c%5E2 where "a" and "b" are the legs of a triangle and "c" is the hypotenuse.


Since the legs are 25 and 12 this means that a=25 and b=12


Also, since the hypotenuse is x, this means that c=x.


a%5E2%2Bb%5E2=c%5E2 Start with the Pythagorean theorem.


25%5E2%2B12%5E2=x%5E2 Plug in a=25, b=12, c=x


625%2B12%5E2=x%5E2 Square 25 to get 625.


625%2B144=x%5E2 Square 12 to get 144.


769=x%5E2 Combine like terms.


x%5E2=769 Rearrange the equation.


x=sqrt%28769%29 Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense).


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Answer:


So the solution is x=sqrt%28769%29 which approximates to x=27.731.